Note---Optimal Inspection Policy in Sequential Screening

Under sequential screening, a production lot is inspected item-by-item; the decision is made after inspecting each item whether to inspect another item or to reject the remainder of the lot; and thus uninspected items are never accepted. This screening process is a special case of the sequential sampling considered in Wortham and Wilson (1971). The process is formulated as an optimal stopping problem using a Bayesian approach. Based on an analysis of the structural properties of the optimal policy, a backward-recursive optimal algorithm, which is more efficient than the existing algorithm for optimal sequential sampling, is developed.